GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO A SEMILINEAR HEAT EQUATION WITH SINGULAR POTENTIAL AND LOGARITHMIC NONLINEARITY

被引：11

作者：

Deng, Xiumei ^{[1
]}

Zhou, Jun ^{[1
]}

机构：

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2020年 / 19卷 / 02期

关键词：

Semilinear heat equation; singular potential; logarithmic nonlinearity; global existence; blow-up; NONEXISTENCE THEOREMS; FILTRATION EQUATION; EVOLUTION-EQUATIONS; PARABOLIC EQUATIONS; INSTABILITY; TIME;

D O I：

10.3934/cpaa.2020042

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper concerns with a semilinear heat equation with singular potential and logarithmic nonlinearity. By using the logarithmic Sobolev inequality and a family of potential wells, the existence of global solutions and infinite time blow-up solutions are obtained. The results of this paper indicate that the polynomial nonlinearity is a critical condition of existence of finite time blow-up solutions to semilinear heat equation with singular potential.

引用

页码：923 / 939

页数：17

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